AN AUTOMORPHISM OF A FREE GROUP OF FINITE RANK WITH MAXIMAL RANK FIXED-POINT SUBGROUP FIXES A PRIMITIVE ELEMENT

Authors
COLLINS DJ TURNER EC
Citation
Dj. Collins et Ec. Turner, AN AUTOMORPHISM OF A FREE GROUP OF FINITE RANK WITH MAXIMAL RANK FIXED-POINT SUBGROUP FIXES A PRIMITIVE ELEMENT, Journal of pure and applied algebra, 88(1-3), 1993, pp. 43-49
Citations number
4
Categorie Soggetti
Mathematics, Pure",Mathematics,Mathematics,Mathematics
Journal title
Journal of pure and applied algebra → ACNP
ISSN journal
00224049
Volume
88
Issue
1-3
Year of publication
1993
Pages
43 - 49
Database
ISI
SICI code
0022-4049(1993)88:1-3<43:AAOAFG>2.0.ZU;2-M
Abstract
We prove that if an automorphism phi of a free group F of rank n has a fixed point subgroup of rank n then phi fixes a primitive element of F. With an appropriate generalisation of rank and primitivity, we prov e the same statement for automorphisms of free products.